Answer
a) See the explanation below.
b) See the explanation below.
c) See the explanation below.
d) See the explanation below.
e) See the explanation below.
Work Step by Step
a) This means that $f(x,y) \leq f(a,b)$ when $(x,y)$ near to the $(a,b)$ and $f$ has a local maximum at $(a,b)$.
b) This means that $f(x,y) \leq f(a,b)$ when $(x,y)$ for all points $(x,y)$ a set of real numbers in the domain $D$ and $f$ has a absolute maximum at $(a,b)$.
c) This means that $f(x,y) \geq f(a,b)$ when $(x,y)$ near to the $(a,b)$ and $f$ has a local minimum at $(a,b)$.
d) This means that $f(x,y) \geq f(a,b)$ when $(x,y)$ for all points $(x,y)$ a set of real numbers in the domain $D$ and $f$ has a absolute minimum at $(a,b)$.
e) This means that $f(x,y)$ has neither a local maximum nor a local minimum or, both are in opposite directions when $(x,y)$ near to the $(a,b)$.
